Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises - Page 908: 35



Work Step by Step

Simplify $$\sec\theta\cos\theta-\cos^{2}\theta.$$ Use the Reciprocal Identity $$\sec\theta=\frac{1}{\cos\theta}$$ to obtain $$\sec\theta\cos\theta-\cos^{2}\theta=\bigg(\frac{1}{\cos\theta}\bigg)\cos\theta-\cos^{2}\theta=1-\cos^{2}\theta.$$ The Pythagorean Identity states $$\sin^{2}\theta+\cos^{2}\theta=1$$ or $$1-\cos^{2}\theta=\sin^{2}\theta.$$ So $$\sec\theta\cos\theta-\cos^{2}\theta=\sin^{2}\theta.$$
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